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Geometric Twins

A bigger copy is a different figure

A drawing is copied at 140%. That means every length becomes 1.4 times as long. Put one drawing on top of the other. They do not match.

Slide the size. Only one size gives a twin.

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The small triangle.
Step 1 of 3
  1. The small triangle.
  2. A 140% copy, from the same corner.
  3. The far corners miss. Corners agree, sides do not.

Congruent needs the sides too

Every side and every corner must match. A bigger copy keeps every corner. Its sides are longer. So it is not congruent.

Example: sides of 40, 50 and 60 mm. Multiply each side by 1.4. 40 × 1.4 = 56 mm. 50 × 1.4 = 70 mm. 60 × 1.4 = 84 mm.

Three copies of one triangle
The copyCornersSidesCongruent?
Same size, movedMatchMatchYes
Turned overMatchMatchYes
Blown up to 140%MatchEvery one longerNo

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This track

  1. 0 Start here
  2. 1 Landing one on the other
  3. 2 Slide it, turn it, flip it
  4. 3 A bigger copy is a different figure
  5. 4 One line, one corner
  6. 5 Three sides settle it
  7. 6 Two sides and the corner between them
  8. 7 Two corners and a side
  9. 8 When shape is not enough
  10. 9 Writing a congruence in order
  11. 10 RHS: a right angle, the hypotenuse, a side
  12. 11 Equal sides, equal angles
  13. 12 Twins hiding in a figure
  14. 13 Checkpoint: order, RHS and angles
  15. 14 The big picture
  16. 15 Track quiz

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